Computer study of ion-trapping instability in microwave tubes

Microwave tubes are known to exhibit low-frequency instabilities due to ion bunching. These instabilities are treated theoretically for an idealised model in two dimensions. The problem is rendered soluble by using supersized charge carriers whose equations of motion are formulated exactly by using complex variable techniques. These equations of motion are integrated numerically to obtain a complete solution of the idealised problem. The results agree with earlier experimental work and support strongly the qualitative theory of the instability. The computations enable one to predict ways of preventing its occurrence.